Subgroups — C₃×#22576417 #39908023

Order 26100.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₂₉×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#10596817	—	3	1	no	maximal
3	#22576417	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₃×C₂₉×C₅²⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅²×D₂₉	D₃	1	1	yes	characteristic
6	D₂₉×C₅²⋊C₃	—	2	1	no	—
7	D₂₉×C₅²⋊C₃	C₂×C₃	1	1	yes	characteristic
8	C₅×#10596817	—	3	1	no	Hall
9	C₂₉×C₅²⋊C₃	—	2	1	no	—
10	C₂₉×C₅²⋊C₃	C₃×C₄	1	1	yes	characteristic, complemented
11	C₃×C₅²×C₂₉	Dic₃	1	1	yes	characteristic, complemented
12	C₃×#10596817	—	3	1	no	—
13	C₃×C₅×#1181	—	15	1	no	—
14	C₅²×D₂₉	C₃×D₃	1	1	yes	characteristic
15	C₃×C₃⋊#1181	—	25	1	no	maximal, Hall
16	C₃×#64470	—	29	1	no	maximal, Hall
17	C₃×C₅×D₂₉	—	6	1	no	—
18	C₃×C₅×D₂₉	—	6	1	no	—
19	C₅²×C₂₉	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
20	#10596817	—	3	1	no	—
21	C₅×#1181	—	15	1	no	—
22	C₃²×D₂₉	—	50	1	no	—
23	C₂×C₃×C₅²⋊C₃	—	29	1	no	—
24	C₃×C₅×C₂₉	—	6	1	no	—
25	C₃×C₅×C₂₉	—	6	1	no	—
26	C₃⋊#1181	—	25	1	no	—
27	C₃×#1181	—	15	1	no	—
28	C₃×C₅×Dic₅	—	87	1	no	—
29	#64470	—	29	1	no	—
30	C₅×D₂₉	—	6	1	no	—
31	C₅×D₂₉	—	6	1	no	—
32	C₃²×C₂₉	—	50	1	no	Hall
33	C₃×C₅²⋊C₃	#1181	1	1	yes	characteristic, complemented, Hall
34	C₃×D₂₉	—	50	1	no	—
35	C₃×D₂₉	—	50	1	no	—
36	C₃×D₂₉	#3874	1	1	yes	characteristic
37	C₂×C₃×C₅²	—	29	1	no	—
38	C₂×C₅²⋊C₃	—	29	1	no	—
39	C₂×C₅²⋊C₃	—	58	1	no	—
40	C₅×C₂₉	—	6	1	no	—
41	C₅×C₂₉	—	6	1	no	—
42	#1181	—	15	1	no	Hall
43	C₅×Dic₅	—	87	1	no	Hall
44	C₃×C₂₉	—	50	1	no	—
45	C₃×C₂₉	—	50	1	no	—
46	C₃×C₂₉	#64470	1	1	yes	characteristic, complemented
47	C₃×C₅²	C₃⋊#1181	1	1	yes	characteristic, complemented
48	C₅²⋊C₃	—	2	1	no	—
49	C₅²⋊C₃	C₃×#1181	1	1	yes	characteristic, complemented
50	C₃×C₄×C₅	—	435	1	no	—
51	C₃×Dic₅	—	87	1	no	—
52	D₂₉	C₃×#3874	1	1	yes	characteristic
53	C₂×C₅²	—	29	1	no	—
54	C₃×Dic₃	—	725	1	no	Hall
55	C₂×C₃×C₅	—	87	1	no	—
56	C₂×C₃×C₅	—	174	1	no	—
57	C₂₉	C₃×#64470	1	1	yes	characteristic, complemented, Sylow
58	C₅²	C₃×C₃⋊#1181	1	1	yes	characteristic, complemented, Sylow
59	C₄×C₅	—	435	1	no	—
60	Dic₅	—	87	1	no	—
61	C₂×C₃²	—	1450	1	no	—
62	C₃×C₅	—	3	1	no	—
63	C₃×C₅	—	6	1	no	—
64	C₃×C₄	—	435	1	no	—
65	Dic₃	—	725	1	no	—
66	C₂×C₅	—	87	1	no	—
67	C₂×C₅	—	87	1	no	—
68	C₃²	—	50	1	no	Sylow
69	C₂×C₃	—	29	1	no	—
70	C₂×C₃	—	1450	1	no	—
71	C₂×C₃	—	1450	1	no	—
72	C₅	—	3	1	no	—
73	C₅	—	3	1	no	—
74	C₄	—	435	1	no	Sylow
75	C₃	—	50	1	no	—
76	C₃	—	50	1	no	—
77	C₃	#22576417	1	1	yes	characteristic, direct product factor
78	C₂	—	29	1	no	—

	subgroup	G/H
center, hypercenter	C₃	#22576417
commutator, hypocenter	C₂₉×C₅²⋊C₃	C₃×C₄
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₂₉	Dic₃
prime radical	C₃×D₂₉×C₅²⋊C₃	C₂
cosocle	D₂₉×C₅²⋊C₃	C₂×C₃
LCS	G ▷ C₂₉×C₅²⋊C₃
UCS	C₁ ◁ C₃

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. #22576417	C₃	direct (N × H)
4. C₃×C₂₉×C₅²⋊C₃	C₄	semidirect
10. C₂₉×C₅²⋊C₃	C₃×C₄	semidirect
11. C₃×C₅²×C₂₉	Dic₃	semidirect
19. C₅²×C₂₉	C₃×Dic₃	semidirect
33. C₃×C₅²⋊C₃	#1181	semidirect
46. C₃×C₂₉	#64470	semidirect
47. C₃×C₅²	C₃⋊#1181	semidirect
49. C₅²⋊C₃	C₃×#1181	semidirect
57. C₂₉	C₃×#64470	semidirect
58. C₅²	C₃×C₃⋊#1181	semidirect
77. C₃	#22576417	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×D₂₉×C₅²⋊C₃	2
C₃×C₅×#10596817	3
#22576417	3
C₃×C₃⋊#1181	25
C₃×#64470	29

Subgroups — C3×#22576417 #39908023

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#22576417 #39908023